Born to a Quaker family in Settle, North Yorkshire, Birkbeck went to school in Sedbergh and then completed his training as a doctor in Edinburgh in 1799. Before practising as a physician, however, he initially embarked on an academic career, being appointed professor of natural philosophy at the Andersonian Institution (today part of the University of Strathclyde) in Glasgow.
After mechanics started asking questions about the apparatus he used in his lectures, he had the idea of holding free, public lectures on the 'mechanical arts' (c 1800-1804). These Saturday evening events proved very popular and continued after his departure to London, leading to the formation in 1821 of the first Mechanics Institute in Glasgow.
Working as a doctor in London, Birkbeck, with others, established the London Mechanics Institute in November 1823 - of which he was the first President. The Mechanics Institute concept was quickly adopted in numerous other cities and towns across the UK and overseas, but his association with the ground-breaking London institution was marked by it being renamed the Birkbeck Literary and Scientific Institution in 1866 (now, as Birkbeck College, part of the University of London).
He died in 1841 and was buried in Kensal Green Cemetery, London. A monument is also to be found in St Akelda’s church in Giggleswick, near his birthplace in Settle.